Systems of coupled PT-symmetric oscillators

Abstract

The Hamiltonian for a PT-symmetric chain of coupled oscillators is constructed. It is shown that if the loss-gain parameter $\gamma$ is uniform for all oscillators, then as the number of oscillators increases, the region of unbroken PT-symmetry disappears entirely. However, if $\gamma$ is localized in the sense that it decreases for more distant oscillators, then the unbroken-PT-symmetric region persists even as the number of oscillators approaches infinity. In the continuum limit the oscillator system is described by a PT-symmetric pair of wave equations, and a localized loss-gain impurity leads to a pseudo-bound state. It is also shown that a planar configuration of coupled oscillators can have multiple disconnected regions of unbroken PT symmetry.

18 pages, 9 figures

References in corpus (4)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Physics and Mathematics of Calogero particles
• Quasi-bound states in continuum
• Critical behavior in ultra-strong-coupled oscillators

Cited by in corpus (3)

• Coupled Oscillator Systems Having Partial PT Symmetry
• Analytic structure of eigenvalues of coupled quantum systems
• Classical Hamiltonian Systems with Balanced loss and gain